French Socialist party candidate Francois Hollande, center, arrives at his campaign headquarters on the morning after the first round of the French presidential elections in Paris, France, Monday, April 23, 2012. Hollande has taken his plodding, undynamic campaign to become France's next president to within spitting distance of victory over the "hyper-president" Nicolas Sarkozy, finishing first in Sunday's initial round of voting.

Two things stand out about the results of the first round of France’s presidential election, which was held yesterday: One is socialist candidate François Hollande’s narrow victory over incumbent Nicolas Sarkozy, which solidifies his position as the favorite to win the May 6 runoff election; the other is the robust performance by the far-right candidate Marine Le Pen, who came in third with a percentage of the vote surpassing even that achieved by her father in 2002—an outcome that shocked France because it placed him second ahead of Socialist candidate Lionel Jospin.

Hollande, 57, seeking to become the first socialist to win the presidency since Francois Mitterrand was re-elected in 1988, won 28.6 percent of the vote—one of the highest first-round tallies for the Left—against 27.1 percent for Sarkozy. Le Pen ended up with 18 percent, while the fiery, Communist-backed Jean-Luc Mélenchon, who many polls projected would fight neck and neck with the National Front candidate for third place, did worse than expected, receiving 11.1 percent. There was disappointment, too, for François Bayrou, the economically liberal, centrist candidate who had hoped to repeat his impressive 2007 performance, when he came in third with 18.6 percent of the vote. This time around, he was unable to reach even half of that, polling at 9.1 percent. His message of fiscal responsibility and the need to cut spending did not resonate with French voters the way the anti-establishment fireworks of Le Pen and, to a lesser extent, Mélenchon did.

It is not unheard of for the candidate who places second in the first round of a French presidential election to eventually defeat his rival in the runoff—it has happened in three out of eight contests since 1965. That said, Sarkozy faces an uphill battle. Five polls that came out after the first-round vote all predict an Hollande victory, with a share of the vote ranging from 53 percent to 56 percent. That is a lot to overcome in two weeks.

In his speech Sunday night, Mélenchon urged his voters to vote for Hollande on May 6, “as if you were voting to make me president,” and it is expected that the vast majority of them—more than 80 percent—will heed the call. In theory, the incumbent could make up the difference by appealing both to the supporters of Marine Le Pen and to those of Bayrou. After all, he has long been known for his hard-line stance on immigration and radical Islam and his emphasis on safeguarding French national identity. These themes are at the core of Le Pen’s candidacy. As for Bayrou, Sarkozy has argued that they share a common approach on cutting deficits and reducing France’s public debt. Expect him, then, both to dial up the rhetoric on border controls, clamp down on immigrants’ benefits and other subjects close to the heart of National Front voters, and to highlight the dangers of fiscal crisis embedded in Hollande’s Keynesian plans to increase public spending in order to kick-start a stagnant economy.

It is a tricky balancing act, set against difficult electoral math, which was made even more forbidding by the president’s failure to win the first-round vote and thus create some momentum for himself. According to Sunday’s polls, between 48 percent and 60 percent of Le Pen voters intend to support Sarkozy in the second round, between 17 percent and 31 percent will go for Hollande, and a sizable slice, ranging from one-fifth to two-fifths, will abstain. Bayrou voters, for their part, are on the whole more likely to vote for the Socialist candidate than the incumbent in the runoff.

What’s more, Sarkozy is going to have trouble appealing at the same time to anti-European nationalists (the National Front favors a French exit both from the euro and from the passport-free Schengen zone) and to pro-European civil libertarians, like many of Bayrou’s supporters. With Le Pen likely to urge her voters to vote blank in the runoff, the more the French president veers to the hard right to attract them, the more likely he is to alienate the centrists. If this happens, not even a pledge to make Bayrou prime minister—something hinted at during the campaign by a number of Sarkozy’s surrogates—would make the difference for Sarkozy: Bayrou would probably not accept, especially given the incumbent’s poor prospects, and even if he did, it is far from clear that his supporters would follow along. The candidate himself stated after the results were announced that he would assume his responsibilities, indicating that, unlike in 2007, he plans not to stay neutral. But it is still an open question which way he will turn.

On balance, then, Hollande, if not quite a shoo-in, is looking toward May 6 with increasing confidence. But if elected, France’s “Mr Normal,” as he has styled himself in juxtaposition against Sarkozy’s hyperactive theatrics, will have a slate of problems to deal with: wobbly public finances, low growth, high unemployment, and a conservative German government that will seek to stymie any efforts he makes to relax the Eurozone’s new fiscal rules and make the European Central Bank less obsessively focused on the sole objective of maintaining price stability. Changing the policy mix in Europe from the bitter cold of austerity to a more temperate, growth-inducing climate will be his biggest challenge. On his success depends not only the future of France but the short- to medium-term prospects of the whole European economy.